Issue 47

E. Mele et alii, Frattura ed Integrità Strutturale, 47 (2019) 186-208; DOI: 10.3221/IGF-ESIS.47.15

In particular the average values (  E1,A

,  E2,A

and  G12,A

) are given: as a function of α, set the value of ρ, in Fig. 17; as a

function of ρ, fixed the value of α, in Fig. 18; as a function of ρ, for different values of α, in Fig. 19. From Fig. 17 it can be observed that, varying α between 0.1 and 0.6,  E1,A

is always smaller than 1, meaning that the axial

stiffness along x 1

of the Voronoi pattern is lower than the one of the regular, “original” hexagonal structure.

In addition, Fig. 18 shows that  E1,A decreases as ρ increases, i.e. the Voronoi patterns are less stiff than the hexagrid counterparts as the relative density increases. For higher levels of irregularity (α>0.7) and low densities, the Fig. 19 reveals that  E1,A increases and becomes greater than 1 (maximum value equal to 108% for α=1 and ρ=0.01); however, for ρ greater than 0.15, a reduction of  E1,A can be observed (minimum value equal to 88% for α=1 and ρ=0.3). A similar trend can be observed for both  E2,A and  G12,A : for low densities (ρ<0.2) the correction factors are always greater than 100%, i.e. the Voronoi specimens are always stiffer than the hexagonal counterparts (Fig. 17), while increasing the density (ρ>0.2 ) both factors  E2,A and  G12,A decrease.

a) b) c)

Figure 17 : Correction factors vs. irregularity parameter for ρ=0.01: a)  E1,A

; b)  E2,A

; c)  G12,A .

a) b) c)

Figure 18 : Correction factors vs. relative density for α=0.5: a)  E1,A

; b)  E2,A

; c)  G12,A .

a) b) c)

Figure 19 : Correction factors vs. relative density for different values of the irregularity parameter: a)  E1,A ; b)  E2,A ; c)  G12,A .

The Figs. 20 a, b and c report the values of  E1,A , respectively, in a three dimensional coordinate system, as a function of α and ρ, and the surfaces that best fit the point distributions. The three surfaces are represented by polynomial expressions, which define  E1,A ,  E2,A and  G12,A as functions of α and ρ, i.e.:   2 2 3 2 i,A 00 10 01 20 11 02 30 21 2 3 3 2 2 3 4 12 03 31 22 13 04 η ρ, α k k α k ρ k α k α ρ k ρ k α k α ρ k α ρ k ρ k α ρ k α ρ k α ρ k ρ f                                    (22) ,  E2,A and  G12,A

202